My mother recently passed away. My father has also passed away. My mother and younger brother were receiving social security benefits checks from my father. Both checks were for the month of January (she was living) and social security claims that they can not take the checks and re-issue them (since its technically her personal assets now) AND her bank will not release the funds to me without being executor of the estate. I do not want to become executor of the estate because I cannot sell the house (its more trouble than its worth)

So what am I supposed to do?
The only option I can see is to debit the money
From the account. I have her card n PIN...
But of course this sounds very illegal.
Its very frustrating to see money sit in a bank
When me and my brother need it so desperately right now.

Withdrawing money from the account would be classed under fraud, however when the death was registered, which I am assuming it has been, the bank account would have been frozen, and they are aware of the death, hence they have explained to you that you need to become executor of your mothers assets, so it would be a wise decision not to attempt it.

A number of factors would influence the direction you need to take, primarily, how old you are.

I would suggest seeking professional legal advice, which is available free of charge from a number of sources.

I don't understand why you don't want to become executor.